Parity of Fourier coefficients of modular forms

Speaker: Professor Scott Ahlgren (University of Illinois at Urbana-Champaign)

Time: 4:00PM
Date: Wed 14th November 2007

Location: Mathematical Sciences Seminar Room

Let f(z) be a modular form (with possible poles at the cusps) whose Fourier coefficients are algebraic integers. We consider the problem of finding lower bounds for the number of odd Fourier coefficients of f. Our result has consequences for a variety of generating functions of number-theoretic and combinatorial interest. In particular, we obtain lower bounds for the number of odd values of the usual partition function p(n).

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)